CN-09 — Whales: the upper bound of animal life, and low-frequency information

What you are building. Two instruments from one animal. First, a method for asking what sets a maximum when the obvious constraint has been removed — buoyancy deletes the bone-stress ceiling that CN-08 spent a chapter deriving, so the blue whale is a controlled experiment in what limit shows up next. Second, a working model of low-frequency sound as a long-baseline information channel, including the units trap that makes most published comparisons of "loudness" wrong. Every number below either carries a source you can check or is written NOT-MEASURED / NOT-CONFIRMED. Nothing here raises any UNI rung — a citation to marine biology is never a UNI gate.

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The headline number has never been measured

Start with the fact that disciplines the whole chapter. Motani & Pyenson (2024), PeerJ 12:e16978, state it flatly: "The body mass of the largest blue whale has never been measured." Not "poorly measured" — never. Every mass you have ever read for a blue whale is one of three things:

1. A piecemeal weighing, biased low. Winston (1950) weighed a 27.1 m female in parts at ≥136.4 tons — "at least", because blood and fluid are lost in butchering.
2. A length→mass regression. Motani & Pyenson compute a 33 m blue whale at 234 t (95% CI 187–294), and correcting for fluid loss give two conditional estimates, each with its own interval: 252 t (95% CI 201–306) correcting for 7% blood loss, and 272 t (95% CI 217–342) correcting for 14%. Note the CI width: the upper bound is nearly double the lower. (The two are not merged here. "252–272 t (CI 201–342)" is a hull of two intervals — a CI no analysis in the paper produced — and it drops the blood-loss assumption that generates each. Collapsing two conditional estimates into one unconditioned interval is the exact error this section exists to teach against.)
3. A volumetric model. Their 3D reconstruction gives 266–279 t, overlapping the regression CI.

The longest reliably measured blue whale was a 33.26 m female (Risting 1928). The famous "190 tonne" figure is a whaling record and is not the largest possible; it is one animal, weighed under industrial conditions, and it is not what the regressions predict for the longest animals.

This is the lesson before any biology: the most-cited number about the largest animal that has ever lived is an extrapolation, and its honest form is an interval, not a point. CN-08's rule holds here exactly — the spread is the result.

The title claim was contested and the challenge failed. Bianucci et al. (2023) described Perucetus colossus, an extinct basilosaurid, at 85–340 t, raising the possibility it outweighed a blue whale. Motani & Pyenson (2024) re-derived it: most likely 60–70 t (at 17 m), maximum 98–114 t (at 20 m), concluding that Perucetus "did not exceed the body mass of today's blue whales." Record this as a live example of the method working in public: an extraordinary claim, a stated method, a re-analysis, a retraction of the extreme. The blue whale keeps the record — for now, and by argument, not by decree.

(Cavity fence, per M22: the 85–340 t figure reached this chapter through Motani & Pyenson's account of it, not from reading Bianucci et al. 2023. It is therefore reported as one side of a dispute as characterised by the other side — which is exactly the position from which a number should not be trusted. Closure: fetch Bianucci et al. 2023 and read the mass estimation directly.)

Buoyancy removes one ceiling. It does not remove the ceiling.

CN-08's constraint is square–cube: bone cross-sectional area grows as L², weight as L³, so stress on the skeleton climbs as L. Immersion cancels the load — a neutrally buoyant animal's skeleton is not carrying it. So the land ceiling is gone. What appears in its place?

Three candidate limits. Only one currently has a direct measurement behind it.

Candidate 1 — foraging energetics (the strongest result). Goldbogen et al. (2019), Science 366(6471):1367–1372, tagged whales across the size spectrum from harbour porpoise to blue whale and computed energetic efficiency (EE) = energy from captured prey ÷ energy expended (including diving costs and post-dive recovery). The result is a divergence, and the divergence is the finding:

• In toothed whales (single-prey feeders), EE falls as body size rises. Bigger odontocetes do eat bigger prey — but "not disproportionally larger". The energy gained per dive fails to cover the rising cost of being large and diving deep.
• In rorquals (lunge filter feeders on krill), EE rises with body size. Each lunge by the largest rorquals engulfs a krill patch whose integrated energy content exceeds the largest toothed-whale prey by at least an order of magnitude, engulfing a volume calculated at 100–160% of the whale's own body volume.
• Balaenids (bowhead, right whales — continuous-ram filter feeders on copepods) show lower EE than rorquals of similar size. Filter feeding alone is not the trick; filter feeding on dense patches is.

The scaling held across simulated metabolic rates from MR ∝ M⁰·⁴⁵ to M⁰·⁷⁵ — i.e. the conclusion does not depend on picking a favourable metabolic exponent, which is the ablation that matters. Their conclusion: "Maximum size in filter feeders is likely constrained by prey availability across space and time." Not by bone. Not by heat. By whether the krill is there.

Candidate 2 — cardiac limits. Goldbogen et al. (2019), PNAS 116(50):25329–25332, put an ECG tag on one blue whale (8.5-hour record). Dive heart rates were 4–8 bpm, minimum 2 bpm — below the allometrically predicted resting rate of 15 bpm for a 70,000 kg animal. Surface rates hit 25–37 bpm, which they place near the maximum possible, and they suggest this "may have limited the evolution of maximum body size."

Carry the tension, do not resolve it. These two papers share a first author and a year. The Science paper says size "does not seem to be limited by physiology... but rather is limited by prey availability." The PNAS paper says cardiac physiology may be the limit. Both are in the table below, tagged OBSERVED-CONTESTED, because that is what they are. n=1 for the heart.

Candidate 3 — thermal. NOT-MEASURED in this pass. A large endotherm in cold water is the easy thermal case (surface-to-volume falls as 3/R; cf. CN-08's gigantothermy). No sourced figure identifies heat as the binding constraint on cetacean size, and none is invented here.

The honest kicker: the biggest animal eats some of the smallest

Here is the part that inverts the intuition. Baleen filter feeding is a low-trophic-level strategy. The blue whale is not the apex of a food chain; it short-circuits one.

The arithmetic is energy flow. Pauly & Christensen (1995), Nature 374:255–257, computed the primary production required to sustain global fisheries using a mean trophic transfer efficiency of 10% — and their phrasing is load-bearing: "a value that was re-estimated rather than assumed", derived from 48 published trophic models spanning six aquatic ecosystem types, with fractional trophic levels from 1.0 (edible algae) to 4.2 (tunas).

Ten percent per rung. Every trophic level up costs you an order of magnitude. A predator at level 4.2 lives on roughly 10⁻³·² of the primary production that a grazer at level 2 can reach. Krill sit near the bottom. Eating them directly, in bulk, is the difference between a landscape that can support a 200-tonne animal and one that cannot.

This is why the ocean can afford a blue whale and the land cannot — and the reason is not buoyancy. It is that no terrestrial habitat presents a dense, mobile, low-trophic-level patch that a large animal can engulf whole. Grass is low-trophic and abundant but it does not aggregate into a bolus you can swallow in one gulp at 100–160% of your body volume; it must be cropped, chewed, and fermented, which is a rate-limited process. The ocean's krill swarms are a pre-concentrated low-trophic resource. Goldbogen et al. call filter feeding "an evolutionary pathway to extremes in body size that are not available to lineages that must feed on one prey at a time."

(Fence: the land-versus-sea contrast in the preceding paragraph is this chapter's synthesis from the Goldbogen and Pauly & Christensen results. It is MODELED reasoning, not a sourced comparative measurement, and it is in the table as such.)

Dive physiology: the solution to a gas problem was to remove the gas

Myoglobin. Noren & Williams (2000), Comp Biochem Physiol A 126(2):181–191, measured skeletal-muscle myoglobin across cetaceans spanning 70 to 80,000 kg: 1.81–5.78 g Mb per 100 g wet muscle. Arregui et al. (2021), Animals 11(2):451, measured up to ~6.3 g·100 g⁻¹ in striped dolphin epaxial muscle, and found locomotor muscles carry 92.8% of total muscle O₂ stores. Against this, non-diving mammals run below ~0.5 g·100 g⁻¹; the comparative literature attributes a 10–30× diver-to-non-diver ratio to Kooyman (1989) — fence: the Kooyman primary was not read in this pass, and an exact human skeletal-muscle value is NOT-MEASURED here. Myoglobin content and body mass together explain 50% of variance in cetacean dive performance, and 83% in odontocetes alone.

Mirceta et al. (2013), Science 340(6138):1234192, supply the mechanism, and it is a beautiful one: you cannot simply make more myoglobin, because concentrated protein precipitates. Ancestral sequence reconstruction across a 130-species phylogeny reveals elevated myoglobin net surface charge in divers — like charges repel, so the molecules stay in solution at concentrations that would otherwise aggregate. The constraint on oxygen storage was never "how much Mb can I express"; it was colloid chemistry, and evolution solved it electrostatically.

Bradycardia. 2–8 bpm on a dive (Goldbogen et al. 2019 PNAS, above). Slowing the pump rations the store.

Lung collapse — and the number people flatten. Ridgway & Howard (1979), Science 206(4423):1182–1183, inferred from intramuscular nitrogen washout in Tursiops truncatus a lung collapse depth of about 70 m, after which gas exchange stops and nitrogen loading ceases. That is the canonical figure. But Moore et al. (2011), J Exp Biol 214:2390–2397, imaged compression directly by hyperbaric CT and extrapolated collapse depth to zero gas volume, getting different, larger numbers: the reported range runs from 58 m (grey seal, lungs at 50% TLC) to 133 m (harbour porpoise, 100% TLC). Every one of those numbers carries a TLC condition, because a lung starting at half its gas volume reaches collapse volume shallower, not deeper — the condition is not decoration, it is the direction of the effect.

(Two fences. (a) "Measured" would be doing work the paper does not support: their vessel is rated only to 170 m depth-equivalent, so the collapse depths are extrapolations to zero gas volume, not readings. (b) Per-specimen values for the common dolphin are NOT-CONFIRMED in this pass — the paper is paywalled, and two independent extraction attempts returned mutually contradictory tables, i.e. no trustworthy witness. An earlier pass of this chapter printed a common-dolphin pair (115 m @ 100% TLC / 127 m @ 50% TLC) that is physically inverted against Boyle's law and against the abstract's own range endpoints, so it was label-swapped or simply wrong; it is removed rather than repaired, because guessing which way to swap it would be inventing a number. Falsifier/closure: fetch Moore et al. 2011 Table 2 and print each value with its species and its TLC condition.)

The specimens were dead. Two methods, two answers, both legitimate, neither refuting the other — one infers from live physiology, one extrapolates from post-mortem mechanics. Do not average them; name the assay. (This is NA-08's kinesin-stall-force lesson in a different animal.)

The design payload stands regardless of which number wins: the whale's answer to decompression sickness is not to manage nitrogen, but to eliminate the compartment that dissolves it. Collapse the alveoli, force air into rigid non-exchanging airways, and the gas cannot enter the blood. You do not regulate the failure mode. You delete its substrate.

The records, told honestly. Schorr et al. (2014), PLOS ONE 9(3):e92633, tagged eight Cuvier's beaked whales (Ziphius cavirostris), logging 3,732 hours and 6,827 dives — 1,142 deep and 5,685 shallow (the 6,827 total is this chapter's sum from the paper's Table; the paper prints the two classes separately, and the figure 6,827 is not itself printed there). The records: 2,992 m and 137.5 min. The mean deep dive is 1,401 m (s.d. 137.8) and 67.4 min (s.d. 6.9) — computed over the 1,142 deep dives only, n = 1,142, not 6,827. Carrying the total into the deep-dive mean overstates its sample by ~6× and silently mixes two dive classes with wildly different durations. Quick et al. (2020), J Exp Biol 223(18):jeb222109, analysed 3,680 dives from 23 tags: median 59.0 min, max 132 min, with 5% exceeding 77.7 min — their behavioural aerobic dive limit estimate.

And then the famous one. The 222-minute dive that made headlines is real — but Quick et al. censored it from their primary dataset, along with a 173-min dive from the same individual (ZcTag066), because they were "recorded 17 and 24 days after a known 1-h exposure to a Navy mid-frequency active sonar signal." The record-breaking dive is a post-sonar-exposure dive. Almost every popular retelling drops that clause, and a number reported without its condition is worth less than the same number with it.

But read what the censoring means, and read it from the authors — not into them. The exclusion is a statistical-hygiene decision for the bADL estimation, not a disturbance verdict. Quick et al. say of these very dives that they are "perhaps more indicative of the true limits of the diving behaviour of this species." The primary authors lean toward capacity. So the honest position is that whether the 222-min dive measures a disturbed animal or a capable one is UNRESOLVED, and both readings are carried here rather than the chapter adopting the one it finds more interesting. The falsifier is the right one either way: an unexposed animal reaching >137.5 min.

Sound: why low frequency is the long-baseline channel

Absorption rises steeply with frequency. Thorp's expression (via the TU Delft OCW propagation reader, ch. 3; primary: Thorp 1967, JASA 42:270) gives α in dB/km for f in kHz:

α = 0.11 f²/(1 + f²)  +  44 f²/(4100 + f²)  +  0.0003 f²

The three terms are boric acid relaxation, magnesium sulfate relaxation, and viscosity. Published values, and the distance to lose 10 dB:

f	α (dB/km)	r₁₀dB
100 Hz	0.0012	8,333 km
1 kHz	0.07	143 km
10 kHz	1.2	8.3 km

Four orders of magnitude in range across two orders in frequency. Extrapolating the same formula down to a fin whale's band (this chapter's own arithmetic, fenced MODELED, and below Thorp's fitting range): at 20 Hz, α ≈ 4.8 × 10⁻⁵ dB/km, giving r₁₀dB ≈ 2.1 × 10⁵ km — about five Earth circumferences. Absorption is simply not the limit down here. For comparison, air at 2 kHz — at 20 °C, 50% RH, 101.325 kPa, per ISO 9613-1 — absorbs at ≈ 9.9 dB/km ≈ 1.14 × 10⁻³ m⁻¹, ≈ 80× more than seawater at the same frequency (Thorp: 1.4 × 10⁻⁵ m⁻¹). The temperature, humidity and pressure are part of the number: an air absorption quoted with no stated condition is a number with no condition, which this chapter's own rail forbids. (Cross-ref NA-06 on frequency; CN-03 on air.)

(Fence, and it cost this chapter its headline: earlier passes printed "air at 2 kHz absorbs at 0.02 m⁻¹, over 1,000× more than seawater" on the authority of the TU Delft OCW reader ch.3, which does say exactly that. The reader's air value is wrong by ~17× and its ratio by ~13× — recorded as a NEGATIVE below. A course reader is not a primary, and this chapter classed it OBSERVED-REPLICATED anyway.)

The SOFAR channel. Sound speed in the sea has a minimum at depth — pressure raises it going down, temperature raises it going up, so there is a turning point (Møhl et al. measured 1477 m/s at the surface falling to 1468 m/s at 500 m in Norwegian coastal water). Rays leaving that axis are refracted back toward it from both sides: the layer is a waveguide, and energy trapped in it never touches the lossy surface or seafloor. Ewing & Worzel (1948), Geological Society of America Memoir 27, demonstrated it — charges detected at up to 900 nmi (~1,700 km). (Fence: axis depth ~750–1,200 m at midlatitudes, shoaling to near-surface in polar regions, is from a secondary source in this pass.)

The units trap — this is where most comparisons die

Underwater dB and airborne dB are different quantities. Underwater sound is referenced to 1 µPa; air to 20 µPa. Two corrections separate them: the reference-pressure ratio (20² = 400) and the acoustic impedance ratio (ρc water / ρc air ≈ 3600). Together:

10 · log₁₀(400 × 3600) = 61.58 dB

So a number quoted "re 1 µPa" is ~62 dB larger than the same physical intensity quoted in air. Møhl et al. (2003) do this conversion themselves: their 235 dB re 1 µPa rms corresponds to 173 dB SPL re 20 µPa in air. This chapter's independent arithmetic gives 235 − 61.58 = 173.4 — agreement with the primary source, which is the only reason it is printed.

Any text comparing a whale to a jet engine without this correction is wrong by ~62 dB. That is not a quibble; it is a factor of ~1.4 million in intensity.

Source levels, with their conventions attached. Širović, Hildebrand & Wiggins (2007), JASA 122(2):1208–1215, using calibrated bottom-moored hydrophones off the Western Antarctic Peninsula: blue whale 189 ± 3 dB re 1 µPa @ 1 m over 25–29 Hz; fin whale 189 ± 4 dB re 1 µPa @ 1 m over 15–28 Hz. They localized blue whales to 200 km (hyperbolic localization, range error 3.8 km) and fin whales to 56 km (multipath, error 3.4 km). Those are measured detection ranges — the distance at which a hydrophone heard a whale, not the distance at which a whale hears a whale.

HONEST FENCE — "whales hear each other across an ocean"

The claim originates with Payne & Webb (1971), Ann. N.Y. Acad. Sci. 188:110–141, "Orientation by means of long range acoustic signaling in baleen whales." What it did: propagate fin-whale-like 20 Hz signals through a deep-sound-channel model and compute the range at which they fall to ambient noise, proposing that baleen whales live in acoustic contact across an ocean basin — the "acoustic herd."

What it did not do: observe two whales communicating at range. It is a calculation. Secondary sources render its headline number as ~700 km, 3,500 miles, 4,000 miles, and 13,000 miles (the last for a pre-propeller ocean) — a spread of more than an order of magnitude, because the answer depends entirely on the assumed noise floor. The primary was not read in this pass, so no specific Payne–Webb range is asserted here. Falsifier/closure: fetch Ann. N.Y. Acad. Sci. 188:110–141 and read the propagation section.

What is measured: whales emit at 189 dB re 1 µPa @ 1 m, and hydrophones detect them at ~10² km (Širović et al. 2007). What is not measured: that a whale receives, recognises, and acts on a conspecific's call at basin scale. Fifty years of anecdote is not a measurement.

The best evidence to date is correlational and recent. Podolskiy, Teilmann & Heide-Jørgensen (2024), Phys. Rev. Research 6:033174, analysed 144 days of dive records from 12 tagged bowhead whales in Disko Bay, West Greenland, and found dive synchronisation at separations up to ~100 km, persisting for up to a week. That is consistent with the acoustic herd hypothesis. It is not a demonstration of it: their tags recorded dives, not sounds, so the acoustic mechanism is inferred from timing correlation, and a shared environmental driver is not excluded.

And the channel is being closed. Andrew et al. (2002), ARLO 3(2):65–70, compared the same receiver off Point Sur, California, across four decades: 1994–2001 levels exceed 1963–1965 by ~10 dB between 20 and 80 Hz and between 200 and 300 Hz, and by ~3 dB at 100 Hz. McDonald, Hildebrand & Wiggins (2006), JASA 120(2):711–718, west of San Nicolas Island: 10–12 dB higher at 30–50 Hz in 2003–2004 than 1964–1966 (95% CI = 2.6 dB), ≈ 2.5–3 dB/decade, tracking a commercial fleet that roughly doubled in number and quadrupled in gross tonnage between 1965 and 2003. Two independent sites, two teams, same direction.

The rise is not band-selective on the published evidence — and an earlier pass of this chapter claimed it was. Both measured rises — Andrew's 20–80 Hz, McDonald's 30–50 Hz — sit at or just above the 15–29 Hz band the blue and fin whales use, and neither team reports a measurement inside that band. Worse for the tidy story: Andrew's second ~10 dB rise at 200–300 Hz sits 7–20× above the whale bands, and it is the one datum the earlier pass omitted — from the prose and from the ΔN_ambient row alike. The honest statement is that the noise rise overlaps the low-frequency channel without being confined to it. Falsifier/closure: a calibrated long-baseline measurement resolving 15–29 Hz specifically.

(A satisfying detail that shows the data are honest rather than tidy: McDonald et al. found the 1960s were louder above 300 Hz, owing to a diel component absent in modern records. A clean "everything got noisier" story would have been more suspicious.)

Toothed whales: convergence down to the amino acid

This is the wing's strongest single receipt for NA-01's doctrine — and its strongest lesson in how far a convergence claim may be pushed.

The earned core. Two independent groups published in the same issue of Current Biology in 2010: Liu et al., 20(2):R53–R54, and Li, Liu, Shi & Zhang, 20(2):R55–R56, "The hearing gene Prestin unites echolocating bats and whales." Prestin is the motor protein of outer hair cells — it is what makes the cochlear amplifier work at high frequency. Build a gene tree from Prestin protein sequences and the bottlenose dolphin lands inside the microbats — contradicting the species phylogeny — with evidence of selection driving the substitutions. Bats and toothed whales, which are not each other's closest relatives by any other evidence, converged on the same molecular solution to the same physical problem. That is not a metaphor about nature's ingenuity; it is a tree topology that contradicts the species tree. (Fence: the bat–cetacean divergence date is NOT-SOURCED in this pass and no figure is asserted here; the argument rests on the topological conflict, which needs no date.)

The overreach, and its correction. Parker et al. (2013), Nature 502(7470):228–231, scaled this up: 22 mammal genomes, 805,053 amino acids across 2,326 orthologous genes, reporting convergence signatures at ~200 loci — a genome-wide phenomenon. Zou & Zhang (2015), MBE 32(5):1237–1241, titled their reply "No Genome-Wide Protein Sequence Convergence for Echolocation" and found the reported signature "largely reflect[s] the background level of sequence convergence unrelated to the origins of echolocation." Their finding: 12 of 14 genuinely convergent sites fell within six of seven already-known hearing proteins — "at most a few proteins were subject to convergent evolution." (Thomas & Hahn 2015, MBE 32(5):1232–1236, attacked the null model on the same page range.)

Read the outcome correctly. The rebuttal did not touch Prestin: Zou & Zhang explicitly preserve it as having passed "proper statistical tests and functional assays." The specific, mechanistically motivated convergence survived; the genome-wide generalisation did not. For NA-01 this is better than an uncontested claim would have been — the doctrine is that convergence under a shared physical constraint is evidence of a constraint-optimum, and what survived is precisely the locus where the constraint bites. What died is the claim that convergence was smeared across the genome, where no constraint argument predicted it.

The loudest sound measured from an animal. Møhl, Wahlberg, Madsen, Heerfordt & Lund (2003), JASA 114(2):1143–1154, using a GPS-synchronised large-aperture array (5–10 units, 14 h) in the Bleik Canyon off Vesterålen: on-axis sperm whale clicks reach 236 dB re 1 µPa rms (eight further events at 226–234 dB; they adopt 235 dB as representative), duration ~100 µs, centroid 15 kHz, directionality index 27 dB, and a half-power half-angle of ~4° — that is, a full −3 dB beamwidth of ~8°. Møhl et al. print the half-angle ("The half power, half-angle of this function is 4°"); beamwidths are conventionally quoted as full width, so "beam width ~4°" is off by 2× against any paper a reader would compare it to. Their own characterisation: these are "by far the loudest of sounds recorded from any biological source."

Why the number was wrong for forty years, and it is a methods story. Early single-hydrophone work reported 170–180 dB and concluded the clicks were weak, long, and non-directional — therefore not sonar. They were recording a 27 dB-directional source off-axis. Large-aperture arrays later found 202–223 dB. Møhl et al. resolved it: only about one click in a thousand recorded is the on-axis monopulse. The "gentle" sperm whale of the classical literature was an artefact of standing in the wrong place. A directional source measured off-axis does not give you a smaller number; it gives you a wrong one.

Two calibration handles from the same paper, both theirs: 235 dB re 1 µPa rms is 10–14 dB above what is measurable 1 m in front of the muzzle of a powerful rifle; and radiating it omnidirectionally would need 2 MW at 100% efficiency — the 27 dB of directionality is what reduces the requirement to a merely astonishing 4 kW.

And Møhl et al. flag the trap themselves: they report true rms, noting it is "significantly different (yielding lower values) from the peak-to-peak measures, used in most of the literature on odontocete clicks." So a sperm whale click and a dolphin click quoted from two papers are frequently not in the same unit. Always read the convention before comparing.

The frequency argument closes the loop. Their detection calculation for a squid (Loligo, target strength −40 dB) gives a detection threshold ~20 dB at 1 km — and they note the absorption term "has a minimal impact due to the relatively low frequencies of the pulse spectrum." Substitute a dolphin-like 100 kHz pulse, all else equal, and detectability falls by ~60 dB at that range. The sperm whale is a long-range sonar because it is a 15 kHz sonar. It pays for the low frequency with a two-metre nose, and buys back the beam width with sheer aperture. The sonar equation itself is developed in CN-10 — it is not duplicated here.

The numbers

Symbol	Value	Units	Scope	Class	Source	Falsifier
M_blue,measured	—	t	mass of the largest blue whale	NOT-MEASURED	Motani & Pyenson 2024, PeerJ 12:e16978	Weigh one intact
M_blue,piece	≥136.4	t	27.1 m female, weighed in parts (fluid lost)	OBSERVED-SINGLE	Winston 1950, via Motani & Pyenson 2024	Re-weigh under controlled loss accounting
M_blue,regr	234 (95% CI 187–294); fluid-corrected 252 (CI 201–306) @ 7% blood loss, 272 (CI 217–342) @ 14%	t	33 m blue whale, length→mass regression. The two fluid-corrected values are separate estimates under separate blood-loss assumptions — never merge them into one interval; "CI 201–342" is a hull of two intervals, not an interval	MODELED	Motani & Pyenson 2024	New regression on a larger measured sample; an independent fluid-loss accounting outside 7–14%
M_blue,vol	266–279	t	3D volumetric model	MODELED	Motani & Pyenson 2024	Independent volumetric model outside range
L_blue,max	33.26	m	longest reliably measured blue whale	OBSERVED-SINGLE	Risting 1928, via Motani & Pyenson 2024	A longer verifiable measurement
M_Perucetus	85–340 vs 60–70 (max 98–114)	t	P. colossus: original vs re-analysis. 85–340 is reported via the rebuttal, not the primary (M22 cavity)	OBSERVED-CONTESTED	Bianucci et al. 2023 as characterised in Motani & Pyenson 2024, PeerJ 12:e16978	Fetch Bianucci et al. 2023 directly; third independent estimate; new postcrania
EE_odontocete	decreases with body mass	ratio	energy captured ÷ energy expended	OBSERVED-REPLICATED	Goldbogen et al. 2019, Science 366:1367–1372	Tag data showing EE rising with size in odontocetes
EE_rorqual	increases with body mass	ratio	lunge filter feeders on krill	OBSERVED-REPLICATED	Goldbogen et al. 2019, Science	As above, inverted
EE_robustness	holds for MR ∝ M^0.45 … M^0.75	—	metabolic-exponent ablation	MODELED	Goldbogen et al. 2019, Science	An exponent in range that flips the sign
V_engulf	100–160	% of whale's own body volume	largest rorquals, per lunge	OBSERVED-REPLICATED	Goldbogen et al. 2019, Science	Direct volumetric measurement outside range
E_lunge/E_prey,odont	≥1	orders of magnitude	largest rorqual lunge vs largest toothed-whale prey	OBSERVED-REPLICATED	Goldbogen et al. 2019, Science	Prey-energy census closing the gap
Size limit	prey availability, not physiology vs cardiac limit	—	Science 2019 vs PNAS 2019, shared first author	OBSERVED-CONTESTED	Goldbogen et al. 2019 Science 366:1367–1372; PNAS 116:25329–25332	ECG on n≫1 blue whales; a prey-abundance manipulation
f_HR,dive	4–8 (min 2)	bpm	blue whale, foraging dives ≤184 m, ≤16.5 min	OBSERVED-SINGLE (n=1)	Goldbogen et al. 2019, PNAS 116(50):25329–25332	Second instrumented blue whale outside range
f_HR,surface	25–37	bpm	post-deep-dive tachycardia, near inferred max	OBSERVED-SINGLE (n=1)	Goldbogen et al. 2019, PNAS	As above
f_HR,pred	15	bpm	allometrically predicted resting, 70,000 kg	MODELED	Goldbogen et al. 2019, PNAS	Re-derive the allometry
TE_trophic	10	% per trophic level	48 trophic models, 6 aquatic ecosystem types; re-estimated, not assumed	OBSERVED-REPLICATED	Pauly & Christensen 1995, Nature 374:255–257	Re-estimate from independent models outside ~5–15%
TL_range	1.0 (edible algae) – 4.2 (tunas)	fractional trophic level	39 commodity groups, global catch 94.3 Mt/yr 1988–91	OBSERVED-REPLICATED	Pauly & Christensen 1995	Re-assign trophic levels
Land-vs-sea size asymmetry	no terrestrial pre-concentrated low-trophic patch	—	this chapter's synthesis	MODELED	Composed here from Goldbogen 2019 + Pauly & Christensen 1995	Exhibit a terrestrial bulk-engulfable low-trophic resource
[Mb]_cetacean	1.81–5.78	g Mb / 100 g wet muscle	cetaceans, body mass 70–80,000 kg	OBSERVED-REPLICATED	Noren & Williams 2000, Comp Biochem Physiol A 126(2):181–191	Measurement outside range under stated method
[Mb]_dolphin,max	~6.3	g Mb / 100 g	striped dolphin, epaxial middle	OBSERVED-SINGLE	Arregui et al. 2021, Animals 11(2):451	Independent assay >2× off
f_Mb,locomotor	92.8	% of total muscle O₂ store	three delphinid species	OBSERVED-SINGLE	Arregui et al. 2021	Re-partition by muscle group
[Mb]_terrestrial	<~0.5 (ratio 10–30× divers:non-divers)	g Mb / 100 g	non-diving mammals — Kooyman 1989 primary not read here	OBSERVED-REPLICATED (secondary attribution)	Kooyman 1989, cited in the comparative literature	Fetch Kooyman 1989; measure human muscle Mb
[Mb]_human	—	g Mb / 100 g	human skeletal muscle	NOT-MEASURED	not sourced in this pass	Fetch a primary value
Z_Mb	elevated net surface charge in divers	—	ancestral reconstruction, 130-species phylogeny	OBSERVED-REPLICATED	Mirceta et al. 2013, Science 340(6138):1234192	A high-[Mb] diver without the charge signature
r²_dive	50 (all cetaceans); 83 (odontocetes)	% variance in max dive duration explained by [Mb] + body mass	—	MODELED	Noren & Williams 2000	Re-run the regression
d_collapse,N₂	~70	m	Tursiops truncatus, live, inferred from N₂ washout	OBSERVED-SINGLE	Ridgway & Howard 1979, Science 206(4423):1182–1183	Repeat washout; a different inferred depth
d_collapse,CT	range 58 (grey seal, 50% TLC) – 133 (harbour porpoise, 100% TLC); per-specimen common-dolphin values NOT-CONFIRMED	m	post-mortem hyperbaric CT, extrapolated to zero gas volume — vessel rated only to 170 m depth-equivalent, so these are extrapolations, not readings. Every value carries a TLC condition. Do not average with the row above	OBSERVED-CONTESTED	Moore et al. 2011, J Exp Biol 214:2390–2397 (abstract only — Table 2 not read in this pass)	In-vivo imaging under pressure reconciling both; fetch Table 2 for per-specimen values
d_dive,max	2,992	m	Ziphius cavirostris, mammalian depth record	OBSERVED-SINGLE	Schorr et al. 2014, PLOS ONE 9(3):e92633	A deeper tagged mammalian dive
t_dive,mean	67.4 (s.d. 6.9) @ 1,401 m (s.d. 137.8)	min	Ziphius, mean deep dive, 8 whales / n = 1,142 deep dives (of 6,827 total = 1,142 deep + 5,685 shallow; the 6,827 sum is this chapter's, from the paper's Table — the paper does not print it). n is the deep-dive count, not the total	OBSERVED-REPLICATED	Schorr et al. 2014	Independent tagging outside range
t_dive,median	59.0 (max 132; 95th pct 77.7 = bADL)	min	Ziphius, 3,680 dives / 23 tags, primary dataset	OBSERVED-REPLICATED	Quick et al. 2020, J Exp Biol 223(18):jeb222109	Independent dataset outside range
t_dive,222	222 (and 173)	min	one individual (ZcTag066); censored from the bADL estimation for statistical hygiene — 17 and 24 d after a known 1-h Navy mid-frequency sonar exposure. Capacity vs disturbance is UNRESOLVED, and the primary authors lean capacity: "perhaps more indicative of the true limits of the diving behaviour of this species"	OBSERVED-CONTESTED (the dispute is capacity-vs-disturbance; the censoring is not a disturbance verdict)	Quick et al. 2020	An unexposed animal reaching >137.5 min
α(f)	0.11f²/(1+f²) + 44f²/(4100+f²) + 0.0003f²	dB/km (f in kHz)	Thorp; N. Atlantic, <50 kHz	OBSERVED-REPLICATED	Thorp 1967, JASA 42:270, via TU Delft OCW reader ch.3	Measured α outside fit under stated conditions
α(100 Hz)	0.0012 → r₁₀dB 8,333	dB/km → km	Thorp, published table	OBSERVED-REPLICATED	TU Delft OCW reader ch.3	Recompute; field measurement
α(1 kHz)	0.07 → r₁₀dB 143	dB/km → km	Thorp, published table	OBSERVED-REPLICATED	as above	as above
α(10 kHz)	1.2 → r₁₀dB 8.3	dB/km → km	Thorp, published table	OBSERVED-REPLICATED	as above	as above
α(20 Hz)	~4.8 × 10⁻⁵ → r₁₀dB ~2.1 × 10⁵	dB/km → km	computed here, Thorp extrapolated below its fitting range	MODELED	Computed here; formula per Thorp 1967	Field measurement at 20 Hz; a low-f formula disagreeing
α(15 kHz)	2.47 (Thorp, evaluated here) vs 1.5 (adopted by Møhl et al. for their sonar-equation example)	dB/km	two model inputs, not two observations. Møhl et al. state no site measurement — 1.5 dB/km is a parameter they plug into a worked example. The gap is an unexplained parameter difference, not a contested observation, and no source cited attributes it to a site effect. Do not reconcile by averaging	MODELED	Computed here (Thorp 1967); Møhl et al. 2003 (parameter choice, not a measurement)	Measure α at 15 kHz at both sites
α_air,2kHz	≈ 9.9 dB/km ≈ 1.14 × 10⁻³ m⁻¹	dB/km; m⁻¹	air at 2 kHz, 20 °C, 50% RH, 101.325 kPa — the condition is part of the number	MODELED (ISO 9613-1 evaluated here)	ISO 9613-1 (the standard, not the course reader); implementation checked against ISO 9613-2 Table 2 (20 °C/70% RH: 1k ≈ 5, 2k ≈ 9, 4k ≈ 23 dB/km)	An ISO 9613-1 table lookup or calibrated air-absorption measurement at 2 kHz disagreeing with ~10 dB/km
α_air/α_water	≈ 80×	ratio	at 2 kHz (air 1.14 × 10⁻³ m⁻¹ @ 20 °C/50% RH vs Thorp 1.4 × 10⁻⁵ m⁻¹). Not ">1,000×" — that figure came from the TU Delft reader's air value, which is wrong by ~17×; see the NEGATIVE below	MODELED (arithmetic on the two source rows)	Computed here from ISO 9613-1 + Thorp 1967	Independent measurement of either term
ΔdB_air/water	61.58	dB	10·log₁₀(20² × 3600): reference-pressure ratio × impedance ratio	MODELED (arithmetic)	Computed here; cross-checked against Møhl et al. 2003's own 235→173 conversion	Arithmetic error; a different impedance ratio
SL_blue	189 ± 3	dB re 1 µPa @ 1 m, 25–29 Hz	calibrated bottom-moored hydrophones, W. Antarctic Peninsula	OBSERVED-REPLICATED	Širović, Hildebrand & Wiggins 2007, JASA 122(2):1208–1215	Calibrated measurement outside 186–192
SL_fin	189 ± 4	dB re 1 µPa @ 1 m, 15–28 Hz	as above	OBSERVED-REPLICATED	Širović et al. 2007	As above
r_detect,blue	200 (error 3.8)	km	measured localization range (hyperbolic) — hydrophone hears whale	OBSERVED-SINGLE	Širović et al. 2007	Longer localization with stated error
r_detect,fin	56 (error 3.4)	km	measured localization range (multipath)	OBSERVED-SINGLE	Širović et al. 2007	As above
SL_sperm	236 max; 235 representative (8 events 226–234)	dB re 1 µPa rms (on-axis)	Physeter, large-aperture array, 14 h, Bleik Canyon	OBSERVED-SINGLE	Møhl et al. 2003, JASA 114(2):1143–1154	Calibrated on-axis measurement outside range
SL_sperm,offaxis	170–180 (classical) vs 202–223 (large-aperture) vs 236 (on-axis)	dB re 1 µPa	the same animal — the spread is aspect angle, not disagreement	OBSERVED-REPLICATED	Møhl et al. 2003 (reviewing Backus & Schevill 1966 etc.)	Show the classical figures were on-axis
SL_sperm,air-equiv	173	dB SPL re 20 µPa	235 dB re 1 µPa rms converted by the source authors	MODELED	Møhl et al. 2003	Recompute the impedance conversion
DI_sperm	27 (half-power half-angle ~4° ⇒ full −3 dB beamwidth ~8°)	dB	composite directionality index. Møhl et al. print the half-angle; beamwidth is conventionally quoted full-width — name the convention or be wrong by 2×	OBSERVED-SINGLE	Møhl et al. 2003	Reconstruct the radiation pattern
p_on-axis	~1 in 1,000	clicks	probability a recorded click is the on-axis monopulse	OBSERVED-SINGLE	Møhl et al. 2003	A recording geometry with a different hit rate
P_sperm	2 MW omni @ 100% eff. → 4 kW at DI = 27 dB	W	peak acoustic power to make 235 dB re 1 µPa rms	MODELED	Møhl et al. 2003	Recompute; refute DI
t_click / f_c	~100 µs / 15 kHz (cBW_rms 4.1 kHz)	s / Hz	on-axis p1 pulse	OBSERVED-SINGLE	Møhl et al. 2003	Independent on-axis recording
rms vs p-p	true rms is significantly lower than peak-to-peak, "used in most of the literature on odontocete clicks"	—	the units trap	OBSERVED-REPLICATED	Møhl et al. 2003 (their own caveat)	—
Δ_100kHz	~60	dB detectability lost to absorption at 1 km	substituting a dolphin-like 100 kHz pulse, ceteris paribus	MODELED	Møhl et al. 2003	Recompute the sonar equation
c_sound	1477 (surface) → 1468 (500 m)	m/s	Norwegian coastal water, measured profile	OBSERVED-SINGLE	Møhl et al. 2003	Independent CTD profile
z_SOFAR	~750–1,200 (midlat); near-surface polar	m	deep sound channel axis	OBSERVED-REPLICATED (secondary source in this pass)	Ewing & Worzel 1948, GSA Memoir 27; depth via secondary	Fetch a primary sound-speed climatology
r_SOFAR,demo	up to 900 nmi (~1,700 km)	km	1944 R/V Saluda explosive-charge demonstration	OBSERVED-SINGLE	Ewing & Worzel 1948	Read the primary; a different demonstrated range
r_PayneWebb	NOT-CONFIRMED (secondaries render ~700 km / 3,500 mi / 4,000 mi / 13,000 mi)	km	calculated basin-scale range for 20 Hz calls	MODELED / NOT-CONFIRMED	Payne & Webb 1971, Ann NY Acad Sci 188:110–141 — primary not read in this pass	Fetch the primary and read the propagation section
Whales hear each other across a basin	—	—	reception + response at basin scale	NOT-MEASURED	—	Show a whale detectably responds to an identified conspecific call at ≥10³ km
r_sync,bowhead	up to ~100 (persisting up to ~1 week)	km	12 tagged bowheads, 144 d, Disko Bay; dives recorded, sounds not	OBSERVED-SINGLE (mechanism inferred)	Podolskiy, Teilmann & Heide-Jørgensen 2024, Phys Rev Research 6:033174	Simultaneous acoustic + dive tags; exclude a shared environmental driver
ΔN_ambient	~10 (20–80 Hz) and ~10 (200–300 Hz); ~3 (100 Hz)	dB, 1963–65 → 1994–2001	same receiver, Point Sur, California. The 200–300 Hz rise sits 7–20× above the whale bands — it is part of Andrew's result and it refutes any "concentrated in the whale band" reading	OBSERVED-REPLICATED	Andrew et al. 2002, ARLO 3(2):65–70	Recalibrate; a site showing no rise
ΔN_ambient,SN	10–12 (95% CI 2.6) at 30–50 Hz ⇒ 2.5–3 dB/decade	dB, 1964–66 → 2003–04	west of San Nicolas Is.; 138 d continuous	OBSERVED-REPLICATED	McDonald, Hildebrand & Wiggins 2006, JASA 120(2):711–718	Independent long-baseline site disagreeing
ΔN_>300Hz	1960s higher (diel component absent today)	dB	the counter-trend — the data are not tidy	OBSERVED-SINGLE	McDonald et al. 2006	Re-analyse the 1960s diel signal
N_ships	~2× count, ~4× gross tonnage, 1965→2003	—	world commercial fleet	OBSERVED-SINGLE	McDonald et al. 2006	Independent fleet statistics
Noise rise vs the whale band	measured rises (Andrew 20–80 Hz; McDonald 30–50 Hz) overlap but are not confined to the 15–29 Hz blue/fin band; neither team reports a measurement inside that band, and Andrew finds a comparable rise at 200–300 Hz	—	this chapter's synthesis — not "concentrated in the whale band", which no cited paper supports	MODELED	Composed here from Andrew et al. 2002 + McDonald et al. 2006 + Širović et al. 2007	A calibrated long-baseline measurement resolving 15–29 Hz specifically
Prestin convergence	dolphin groups inside microbats in the Prestin protein tree	—	echolocating bats + toothed whales	OBSERVED-REPLICATED	Li, Liu, Shi & Zhang 2010, Curr Biol 20(2):R55–R56; Liu et al. 2010, 20(2):R53–R54 (independent, same issue)	A Prestin tree recovering the species topology
Genome-wide convergence	~200 loci (Parker) vs "background level" (Zou & Zhang)	loci	22 genomes, 805,053 aa, 2,326 genes	OBSERVED-CONTESTED (the genome-wide claim did not survive)	Parker et al. 2013, Nature 502(7470):228–231; Zou & Zhang 2015, MBE 32(5):1237–1241; Thomas & Hahn 2015, MBE 32(5):1232–1236	A method settling the null model
Hearing-gene convergence	12 of 14 convergent sites in 6 of 7 known hearing proteins; Prestin explicitly upheld	sites	Zou & Zhang's own re-analysis	OBSERVED-REPLICATED	Zou & Zhang 2015	Re-analysis dispersing the sites genome-wide

Falsifier (operable)

This chapter's central structural claim — that the ceiling on animal size, once buoyancy removes the skeletal-stress constraint, is set by the energetics of acquiring a low-trophic-level resource in bulk, not by the mechanics of being large — is refuted by exhibiting either:

1. A large aquatic animal whose foraging energetic efficiency rises with body size and which nevertheless does not approach the size ceiling, with prey demonstrably abundant across its range and season — which would show prey availability is not binding; or
2. A direct measurement identifying a mechanical, cardiac, thermal, or respiratory ceiling that binds at a mass below ~250 t — e.g. ECG on a statistically adequate sample of blue whales showing surface heart rate saturating at a mass well under the observed maximum. (Goldbogen et al. 2019 PNAS is n=1 and is a candidate for this falsifier, not a satisfaction of it.)

The low-frequency channel claim — that the useful long-baseline information channel in the sea is low-frequency because absorption scales steeply with frequency — is refuted by a calibrated field measurement of α at 20–100 Hz exceeding the Thorp/Francois–Garrison predictions by more than an order of magnitude, or by demonstrating a >10³ km biological signalling channel above 10 kHz.

Row-local falsifiers are in the table. A refuted row moves that row. A refuted EE-versus-size divergence, or a refuted α ∝ f², moves the chapter.

Recorded INADMISSIBLE / NEGATIVE (first-class, inline)

• "Whale calls can be heard across an ocean" / "whales talk to each other across the globe." — NOT-MEASURED as stated, and routinely presented as if measured. Payne & Webb (1971) calculated a basin-scale range; they did not observe reception. Fifty years on, the best evidence remains correlational (Podolskiy et al. 2024: dive synchrony to ~100 km, with sounds not recorded). The measured quantities are a 189 dB re 1 µPa @ 1 m source level and ~200 km hydrophone localization. Emission is not communication, and detection by an instrument is not reception by an animal. Recorded as an open question with a stated falsifier, not as folklore and not with contempt — Payne & Webb's model was good science that has simply never been closed.
• NEGATIVE / units trap — comparing underwater dB to airborne dB directly. Wrong by 61.58 dB (~1.4 × 10⁶ in intensity). "The sperm whale is louder than a jet engine" is not a finding; it is a missing impedance correction. Møhl et al. (2003) do the conversion themselves: 235 dB re 1 µPa rms = 173 dB SPL re 20 µPa. Recorded because the error is near-universal in popular accounts.
• NEGATIVE / units trap — rms versus peak-to-peak. Møhl et al. report true rms and warn it is "significantly different (yielding lower values) from the peak-to-peak measures, used in most of the literature on odontocete clicks." Quoting a sperm whale click against a dolphin click across two papers is frequently a comparison between different units. Named by the primary source itself.
• NEGATIVE / units trap — half-angle versus full beamwidth. Møhl et al. print "a half-angle, half-power beam width of about 4°". Beamwidths are conventionally quoted as full width, so the sperm whale's −3 dB beam is ~8° — and an earlier pass of this chapter printed "half-power beam width ~4°", wrong by 2× against any paper a reader would compare it to. Same class of error as re 1 µPa-vs-re 20 µPa and rms-vs-p-p, and committed while quoting the very source that supplies the warning, in the section devoted to warning about it. Recorded as the third instance because the pattern is the point: a convention is not a detail, and the trap catches the people who know about the trap.
• NEGATIVE / a teaching source's order-of-magnitude error, laundered here as OBSERVED-REPLICATED. The TU Delft OCW propagation reader (ch.3) states verbatim: "For 2 kHz this is 0.02 m-1, which is over a factor 1000 larger than in seawater at the same frequency (Thorpe: 1.4x10-5 m-1)." The reader's air value is wrong by ~17×. Its own conversion on the same page — α(dB/km) = 8686·α(m⁻¹) — turns 0.02 m⁻¹ into 174 dB/km at 2 kHz, which is physically absurd. ISO 9613-1 evaluated here (2 kHz, 20 °C, 50% RH, 101.325 kPa) gives 9.87 dB/km = 1.14 × 10⁻³ m⁻¹; and 0.02 m⁻¹ is in fact the ISO air value at ~10 kHz (1.83 × 10⁻² m⁻¹), so the reader appears to have mislabelled a 10 kHz value as 2 kHz. The true ratio is ≈ 81×, not >1,000×. Recorded twice over: against the reader, whose error is carried into the wider literature; and against this chapter, which transcribed it faithfully, classed it OBSERVED-REPLICATED — the strongest NATURA class — with no primary read and no secondary-source fence (while fencing z_SOFAR and [Mb]_terrestrial correctly on the same page), and staked its entire low-frequency thesis on an air/water contrast it had wrong by ~13×. A faithful transcription of a wrong number is still a wrong number, and fidelity to a secondary is not evidence.
• NEGATIVE / the censored record — and this chapter's own misreading of what the censoring meant. The widely reported 222-minute Cuvier's beaked whale dive was excluded from Quick et al.'s own analysis — it and a 173-min dive came from one individual 17 and 24 days after a known Navy mid-frequency sonar exposure. Reporting the number without that condition is reporting a number without its scope, and popular retellings do exactly that. But an earlier pass of this chapter glossed the censoring as meaning the dive "may be evidence of disturbance, not capacity", called the ordinary reading an inversion of the source's meaning, and attributed all of that to Quick et al. The authors hold the opposite view. They write that these extreme durations are "perhaps more indicative of the true limits of the diving behaviour of this species", and they censored them for statistical hygiene in the bADL estimation — not on suspicion of disturbance. Capacity vs disturbance is UNRESOLVED, and the primary authors lean capacity. Recorded as a NEGATIVE against this chapter: presenting one's own inference as the cited authors' position — and then accusing everyone else of inverting them — is precisely what M22 exists to stop, and it was committed in a chapter whose stated doctrine is read the primary, as its flagship NEGATIVE. The uncensored figures are median 59.0 min, max 132 min, bADL ≈ 77.7 min.
• NEGATIVE / genome-wide echolocation convergence. Parker et al. (2013)'s ~200-locus genome-wide signature did not survive: Zou & Zhang (2015) found it "largely reflect[s] the background level of sequence convergence unrelated to the origins of echolocation." Recorded as a published negative, and recorded as a success of the method under M15 — the specific, mechanistically motivated Prestin result stands precisely because someone tried to break the general one and could not break the specific one.
• NEGATIVE / off-axis measurement of a directional source. Forty years of literature described sperm whale clicks as weak (170–180 dB), long, and non-directional, and inferred from those properties that the clicks were not sonar. The source has DI = 27 dB and only ~1 click in 1,000 is recorded on-axis. The error was not in the instruments; it was in the geometry, and it propagated into a wrong functional conclusion for four decades.
• INADMISSIBLE — "the blue whale is nature's most efficient/perfect design." Unfalsifiable as stated: no observation is specified that could refute it. The falsifiable neighbours are in the table (EE rises with size in rorquals; falls in odontocetes) and are what should be cited instead. Recorded, not mocked.
• NEGATIVE / cavity (M22). Perucetus's 85–340 t is reported here only through the paper that rebuts it. That is a cavity: the rebuttal is not a neutral witness to the claim's strength. The dispute is recorded; the original number is not endorsed at any confidence, in either direction. Named because the tidy version of this story ("Perucetus was 340 t, then it wasn't") would be built entirely out of one side's characterisation of the other.
• NOT-CONFIRMED in this pass: Payne & Webb's specific calculated range (secondaries disagree by >10×); Kooyman (1989)'s primary myoglobin comparison; the SOFAR axis depth (secondary source); the "190 t / 27.6 m, 1947" whaling record (secondary source); Bianucci et al. 2023's primary mass estimate (read only via its rebuttal); the bat–cetacean divergence date (no figure asserted); Moore et al. 2011's per-specimen lung-collapse depths for the common dolphin (paper paywalled, Table 2 not read; two independent extraction attempts returned mutually contradictory tables, so there is no trustworthy witness — only the abstract's range endpoints, 58 m grey seal @ 50% TLC and 133 m harbour porpoise @ 100% TLC, are confirmed, and the previously printed dolphin pair was physically inverted against Boyle's law and has been removed rather than guessed at). Each is printed with that status rather than laundered into a clean number.
• NOT-MEASURED: the mass of the largest blue whale; human skeletal-muscle myoglobin; any thermal ceiling on cetacean body size; whether any whale receives and acts on a conspecific call at basin scale.

HONEST FENCE — MODELED

This chapter is fenced MODELED. Individual rows carry their own classes — many OBSERVED-REPLICATED, several OBSERVED-CONTESTED (Perucetus mass; the size-limit mechanism; lung-collapse depth; genome-wide convergence; the censored 222-min dive), several NOT-MEASURED — but the chapter as an artifact composes measured constants through stated assumptions to reach design conclusions. The assumptions are the fence: the α(20 Hz) row extrapolates Thorp's formula below its fitting range; α_air,2kHz is ISO 9613-1 evaluated here at one stated condition (20 °C, 50% RH, 101.325 kPa) and moves with temperature and humidity; α(15 kHz) compares two model inputs, not two observations; the air/water dB offset assumes plane waves and a nominal impedance ratio of 3600; the land-versus-sea size asymmetry and the noise-rise-versus-whale-band overlap are this chapter's own syntheses, not sourced comparative measurements. Two of the headline results rest on n=1 (the blue whale ECG) or on inference rather than observation of the mechanism (bowhead synchrony).

Per Gould & Lewontin (1979), "The Spandrels of San Marco and the Panglossian Paradigm": nothing above establishes that any cetacean feature is an optimum. Drift, phylogenetic inertia, developmental constraint, and frozen accidents produce traits that solve nothing — and cetaceans carry conspicuous ones, having re-entered the water with an air-breathing tetrapod body plan that a designer starting fresh would never choose. Nature's authority here is precise and narrow: it has already run a very long parallel search under real physical constraints in which the failures were deleted. That makes the bat–whale Prestin convergence evidence of a constraint-optimum at that locus — and makes every number above a hypothesis generator, not a proof. Per repo rule M7, any design taken from this chapter must still beat a tuned conventional baseline on a pre-registered metric, with a discriminator that would collapse the gain, or it is recorded NEGATIVE.

Not claimed

• Not claimed: that whales communicate across ocean basins. That is the chapter's flagship NOT-MEASURED and it has an operable falsifier. The measured facts (189 dB source levels, ~200 km localization, ~100 km dive synchrony) do not add up to it, and stacking them until they seem to is the exact error this chapter exists to prevent.
• Not claimed: that prey availability is the blue whale's size limit. Goldbogen et al. (2019, Science) argue it; Goldbogen et al. (2019, PNAS) point at cardiac limits. Both are carried; neither is adopted. A chapter that picked one would be more satisfying and less honest.
• Not claimed: that lunge feeding is "optimal", or that filter feeding is a general route to gigantism. Balaenids filter-feed and show lower efficiency than similarly sized rorquals — the mechanism is bulk engulfment of dense patches, and the counterexample is inside the same clade.
• Not claimed: that the sperm whale's 236 dB is comparable to any airborne figure without the 61.58 dB correction, or to any peak-to-peak odontocete figure without a convention check.
• Not claimed: that echolocation convergence extends genome-wide. It does not; that claim was published and rebutted, and both are cited.
• Not claimed: that any whale is self-aware, cognitive, linguistic, or that whale song constitutes language. Nothing in this chapter measures any such thing. Source levels, call bands, dive timing, and gene trees are what were measured; they license no claim about experience, and the honest position on cetacean minds is that this chapter does not address it.
• Not claimed: that any citation above raises any UNI rung. A nature citation is NEVER a UNI gate. Reading Møhl et al. 2003 does not make any UNI claim proven, designed, or built. The NATURA twelve-value class (OBSERVED-REPLICATED / OBSERVED-SINGLE / OBSERVED-CONTESTED / MODELED / MODELED-CONTESTED / HYPOTHESIZED / INADMISSIBLE / SUPERSEDED / NOT-MEASURED / NOT-SOURCED / NOT-CONFIRMED / NOT-LOCATED — six of them registered by NA-00 amendment 2026-07-15-A) and the UNI four-value fence (proven / designed / hypothesized / not-yet-built) describe different kinds of claim and never merge. This chapter contains zero UNI claims.
• QUAESTIO-APERTA: "the next evolution beyond human" and "full human" appear nowhere in this chapter as a target, milestone, or deliverable. They are permanent open questions, and the upper bound of animal size has no bearing on them.